From left, students Labaron Scott, 10, Jalen Reed, 9, and Christian Robinson, 9, show support for Chicago teachers. (Reuters)

Monday, I passed along the Chicago Public Schools' estimate of the mean teacher salary, which is $74,839. Pro-union sources are objecting, with some putting the figure at $56,720, almost $20,000 below CPS' estimate. So is the school district just lying about this?

Nope. The union allies are right to look at medians, and the CPS number is slightly out of date, but $74,839 is closer to the right answer than $56,720.

The $56,720 number is the median salary for teachers in what the Bureau of Labor Statistics dubs the "Chicago-Joliet-Naperville, IL Metropolitan Division." This includes not only Cook County, which includes all of the Chicago (and thus all of the Chicago Public School district), but also suburbs and other outlying towns like Burbank, Chicago Heights and Park Ridge, as well as six other counties: DeKalb, DuPage, Grundy, Kane, Kendall, McHenry and Will.

Using the Census's 2011 estimates, the population in those seven counties is about 7 million (or 6,999,344 to be precise) as opposed to 2,707,120 in Chicago alone. So the $56,720 figure assumes that we can extrapolate salary patterns in Chicago from those of a region more than two-and-a-half times its size. That's a questionable methodology, to say the least.

Luckily, we don't have to guess, since CPS publishes median salary statistics (see page 198 in this pdf). As is often the case with stats like these, the median salary is below the mean: for the 2010-11 school year, the most recent year for which data is available, the median salary was $67,974, as opposed to the mean of $74,236 that year (as reported, pdf, by the Illinois State Board of Education). That mean is slightly different than the one reported by CPS because it relies on more recent ISBE data.

Some of that salary has to go to pension contributions. Teachers are required to contribute 9 percent of their salary to their pensions, and support personnel must contribute 8.5 percent, as opposed to 6.2 percent if they were part of the Social Security system. But the Chicago Public Schools system pays for 7 percent of the employee contribution. So the more relevant comparison is a 1.5 to 2 percent contribution for CPS employees compared to 6.2 percent for private sector workers paying Social Security tax. So the median after-pension income is $66,614, which a private sector employee on Social Security would need to earn $71,017 a year to make. So a median of $71,017 (or a mean of $77,560) is the most relevant number for comparing Chicago public school teachers to other workers.

What about the longer school day that Chicago Mayor Rahm Emanuel is implementing? The school day is increasing from five hours and forty-five minutes for elementary school and seven hours for high school, to seven and seven and a half hours, respectively. Isn't an increase in hours of that scale effectively a wage cut, in per-hour terms?

Not a big one. Under a deal reached by Emanuel and the Chicago Teachers' Union in July, almost 500 new teachers will be hired to enable the new schedule, and while high school teachers will have to work another 14 minutes every day, elementary and middle school teachers' hours won't change at all. So the overall effect on per-worker hours is minimal.

None of this is to say anything about whether the average teacher's salary is at the right level. It's just to say that a fair read of the numbers suggests that $71,017 is a much more accurate estimate of what a typical Chicago public school teacher makes than $56,720.